please send complete handwritten solution for Q 3 1.Give complete definitions of the following terms.a.a linear combination of v,...,V_{k}b.the Span of a set of vectors S={v,...,v_{k}}c.a linearly independent set S={v,.v_{k}}d.a subspace We.the orthogonal complement of a subspace W of R".f.a basis for W2Indicate if the statement is True or False, and give a brief explanationwhy.a.A set of 7 vectors from a 7-dimensional subspace is linearly independent.b.A set of 11 vectors from an 5-dimensional subspace is linearly dependent.c.lf S={v,,V2} is a set of two non-zero vectors from R', then Span(S) is a line or a plane throughthe origin.Let S={<5,2,-5>,<7,-3,2>,<13,1,-8>,<9,6,-15>}aDecide whether or not the vector b=<2,0,0> is a member of Span(S).'f b is indeed a member of Span(S), then express it as a linear combination of thevectors in S.с.Is the set S linearly independent or not? Explain your answer.d.Give a basis for W=Span(S) consisting of original members of S.

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Let S={<5,2,-5>,<7,-3,2>,<13,1,-8>,<9,6,-15>} a Decide whether or not the vector b=<2,0,0> is a member of Span(S). !f b is indeed a member of Span(S), then express it as a linear combination of the vectors in S. с. Is the set S linearly independent or not? Explain your answer. d. Give a basis for W=Span(S) consisting of original members of S.

Let S={<5,2,-5>,<7,-3,2>,<13,1,-8>,<9,6,-15>} a Decide whether or not the vector b=<2,0,0> is a member of Span(S). !f b is indeed a member of Span(S), then express it as a linear combination of the vectors in S. с. Is the set S linearly independent or not? Explain your answer. d. Give a basis for W=Span(S) consisting of original members of S.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...

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